Probabilistic calibration of model parameters with approximate Bayesian quadrature and active machine learning
Pengfei Wei, Masaru Kitahara, Matthias G.R. Faes, Michael Beer
Abstract
The calibration of computational models using experimental or operational data to achieve accurate predictions is widely recognized as a crucial challenge in reliability engineering. Bayesian model updating (BMU) has been developed as an appealing methodological framework to achieve this goal, but existing methods range from very approximate but cheap (e.g. Laplace approximation and conjugate priors), less approximate and a bit cheaper (e.g. approximate Bayesian computation), to quite expensive and highly informative techniques such as full Bayesian computation. The goal of this work is to achieve full Bayesian accuracy at a low cost. The approximate Bayesian quadrature has emerged as a highly appealing scheme to achieve this goal. In this work, we develop a family of new acquisition functions with closed-form expressions to accelerate the approximate Bayesian quadrature for addressing the BMU problem with the desired level of accuracy. The proposed method leverages information revealed by both the mean predictions and the posterior covariance of the probabilistic regression model trained for approximating the likelihood function. It thus provides a better trade-off between exploration and exploitation. Results from both numerical and engineering examples show that the proposed method is applicable to multimodel problems, achieving high accuracy and efficiency.